Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690836 | C2 | semidirect |
| 2. #20261285 | C2 | semidirect |
| 3. #20261122 | C2 | semidirect |
| 4. #20261111 | C2 | semidirect |
| 5. #20261107 | C2 | semidirect |
| 6. C4×#13095495 | C2 | semidirect |
| 7. C2×#127×C97 | C2 | semidirect |
| 10. C2×#13095499 | C22 | semidirect |
| 11. C2×#13095496 | C22 | semidirect |
| 13. #15690810 | C22 | semidirect |
| 14. #15690807 | C22 | semidirect |
| 15. #15690798 | C22 | semidirect |
| 18. #15690721 | C22 | semidirect |
| 19. C4×#11715895 | C22 | semidirect |
| 34. #13095495 | D4 | semidirect |
| 71. #11715895 | C2×D4 | semidirect |
| 82. C4×C97 | AGL(1,ℤ/8) | semidirect |
| 91. C97 | #3151 | semidirect |
| 94. C2×#127 | D97 | semidirect |
| 174. C4 | #15690836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690836 | 2 |
| #20261285 | 2 |
| #20261122 | 2 |
| #20261111 | 2 |
| #20261107 | 2 |
| C4×#13095495 | 2 |
| C2×#127×C97 | 2 |
| #3151 | 97 |